Traveling wave based single end fault location

ABSTRACT

Traveling wave information from a single end of an electric power delivery system is used to determine a fault location on a power line of the electric power delivery system. Hypotheses of which of a plurality of received traveling waves represents a first reflection from the fault are evaluated. A determination of an arrival time of the first reflection from the fault is used to calculate a distance from the single end of the power line to the fault location.

RELATED APPLICATION

This application is a continuation of U.S. patent application Ser. No.15/806,959 filed on Nov. 8, 2017, titled “Traveling Wave Based SingleEnd Fault Location” that claims priority under 35 U.S.C. § 119 to U.S.Provisional Patent Application No. 62/420,977 filed on Nov. 11, 2016,also titled “Traveling Wave Based Single End Fault Location,” each ofwhich is hereby incorporated by reference in its entirety.

TECHNICAL FIELD

This disclosure relates to determining a location of a fault usingsingle-end traveling wave information in an electric power deliverysystem.

BRIEF DESCRIPTION OF THE DRAWINGS

This disclosure includes illustrative embodiments that are non-limitingand non-exhaustive. Reference is made to certain of such illustrativeembodiments that are depicted in the figures described below.

FIG. 1A illustrates an example of an intelligent electronic device(IED), according to several of the embodiments described herein.

FIG. 1B illustrates a block diagram of the inputs, parameters, andoutputs of a single-ended traveling wave fault location system, such asmay be implemented by the IED in FIG. 1A.

FIG. 2 illustrates an example of a Bewley lattice diagram that includesa substation, local terminal, fault location, and a remote terminal.

FIG. 3 illustrates a flowchart including inputs and parameters forperforming operations of a method for calculating a fault location.

FIG. 4 illustrates a flowchart of an example of a method for calculatinga fault location.

FIG. 5 illustrates a flowchart of portion of a method for calculating afault location.

FIG. 6A illustrates a Bewley lattice diagram showing TPK(0), F(1), andR(1) based on a hypothesis associated with TPK(1), according to oneembodiment.

FIG. 6B illustrates a Bewley diagram with traveling waves in dashedlines that originate from substation reflections, according to oneembodiment.

FIG. 7 illustrates a portion of a method for calculating expectedtraveling waves for each hypothesis.

FIG. 8A illustrates an example of expected traveling waves from afault-local-fault-local traveling wave reflection pattern in a Bewleylattice diagram.

FIG. 8B illustrates an example of expected traveling waves from afault-remote-fault-local traveling wave reflection pattern in a Bewleylattice diagram.

FIG. 8C illustrates an example of expected traveling waves from afault-local-fault-remote-fault-local traveling wave reflection patternin a Bewley lattice diagram.

FIG. 9 a plurality of expected traveling waves at a local terminal for avector of expected traveling wave arrival times, Th.

FIG. 10 illustrates a portion of a method for calculating a faultlocation based on evaluated hypotheses, according to one embodiment.

FIG. 11 provides a schematic diagram for a simulation to illustrate aspecific example of the systems and methods described herein, accordingto one embodiment.

FIG. 12 illustrates the alpha currents, smoothed via a differentiatorsmoother, for the simulated fault with the corresponding VAL or FALindications for each peak.

FIG. 13 illustrates a table of a calculated modal offset value, IMOFF.

FIG. 14 illustrates a table with the interpolated arrival time stamps(ITPIs), and their corresponding estimated signed magnitudes, IMAG, forthe simulation.

FIG. 15 illustrates a table with interpolated arrival times (TPKs)referenced to the arrival time (TPK) of the first received peak.

FIG. 16 illustrates a table showing the sign, TPSIGN, of each peak withrespect to the first VPK based on the signed value VPK of each peak.

FIG. 17 illustrates a table showing the number matches within a set oftime differences of pair-combinations of TPK values for the F(H) and theR(H) of each hypothesis.

FIG. 18 illustrates a table showing calculated total errors for NM(H)and N1_M(H) within a TWTOL1 parameter.

FIG. 19 illustrates a table showing the first reflection from the faultunderlined, the first reflection from remote station double underlined,and filtered values in strikethrough.

FIG. 20 illustrates a graphical representation of the measured TPKs andthe arrival times of expected traveling waves (ETWs) for threehypotheses with matches identified by circles.

FIG. 21 illustrates a table showing the scores, NS(H), based on TPKmatches with the ETWs for each hypothesis.

FIG. 22 illustrates a table of the total errors for the scores, NS(H),within a 5 μs threshold range.

FIG. 23 is a table showing a weight, WGHT(H), assigned to each of threehypotheses based on an R(H) match with a received TPK value and theNS(H) of each hypothesis.

FIG. 24 includes a table with N values and the total per unit error,ERRpu, for each of the three hypotheses.

FIG. 25 shows the expected reflections for a fault at m=0.3 and thecorresponding TPK measurements as circles.

DETAILED DESCRIPTION

The systems and methods described herein relate to determining alocation of a fault in an electric power delivery system based onmeasurements from a single end of the electric power delivery system.Any of a wide variety of systems and methods may be used to obtaincurrent and/or voltage measurements from an electric power deliverysystem. The system may calculate traveling wave information, such aspolarity, magnitude, and/or time of traveling waves observed at a localend (i.e., first location) of the electric power delivery system. Thesystem may identify a plurality of the received traveling waves as beingpotentially the first received reflection from the fault location.

A traveling wave detector, comprising software, hardware, and/or acombination thereof may be configured to detect arrival times (TPKs) oftraveling wave peaks (VPKs). Each of the plurality of TPKs associatedwith the VPKs that match a polarity of the first received VPK may beconsidered and evaluated (i.e., considered as a hypothesis) to determineif it corresponds to the arrival time of the first received travelingwave peak reflection from the fault location.

The system may utilize one or more types of fault location information,including any one or combination of (i) multi-end traveling wave faultlocation information, (ii) multi-end impedance-based fault locationinformation, and (iii) single-end impedance-based fault locationinformation to establish an initial guess, m_ini, of a location of thefault.

For example, if multi-end traveling wave fault location information isavailable, an initial estimate of the fault location, m_ini, may be madebased on the multi-end traveling wave information; otherwise, ifmulti-end impedance-based fault location is available, an initialestimate of the fault location, m_ini, may be made based on themulti-end impedance-based fault location; otherwise, if single-endimpedance-based fault location information is available, an initialestimate of the fault location, m_ini may be made based on thesingle-end impedance-based fault location information.

If none of these three types of fault location information types areavailable, an initial estimate of the fault location, m_ini, may beassigned by default. For example, m_ini may be set equal to 0.5 in perunit length. In some cases, the single-end traveling wave fault locationmethod may use the initial estimate to determine a possible faultedsection.

Generally speaking, traveling waves couple between faulted and healthyphases as they travel along the line in two sets of aerial modes (alphaand beta) and a ground mode. The alpha mode can be a good representationof the three phase traveling waves for ground faults and can becalculated for any faulted phase. The beta mode can be a goodrepresentation of the three phase traveling waves for phase to phasefaults. The mode (alpha or beta) with the highest current magnitude (oralternatively, voltage in some embodiments) may be used. In someembodiments, a specific mode may be used to detect a specific fault type(e.g., if a fault type is known or identified by a fault detectionsystem).

As described below, arrival times (TPKs) of traveling wave peaks (VPKs,)received at a local terminal may be used to calculate a fault location.The system may identify the reflection path of VPKs detected at thelocal terminal by matching patterns and/or expected arrival times basedon an evaluation of hypotheses, where each hypothesis is considered as apotential TPK corresponding to the VPK from the first reflection fromthe fault location back to the local terminal. A hypothesis for thefault location that results in accurate predictions of traveling wavepeak arrival times (TPKs of VPKs) can be used to calculate an exact orapproximate fault location relative to the local terminal.

In various embodiments, a ruler evaluation (i.e., a repeating traveltime “RTT” evaluation) can be used to evaluate each hypothesis based onthe expected and received traveling waves. In other embodiments, a scoreevaluation (i.e., an expected traveling wave “ETW” evaluation) approachcan be used to evaluate each hypothesis based on the expected andreceived traveling wave. In still other embodiments the ruler (RTT) andscore (ETW) methods may be used in combination.

In some embodiments, the hypotheses may be weighted and evaluated basedon the degree of match (i.e., an error rate) between calculated orexpected traveling waves and measured or received traveling waves.Hypotheses may be rejected based on the number of matches being below athreshold (such as where the number of matches is zero). A faultlocation can be calculated based on the hypotheses with expectedreflections that most closely match received reflections.

The systems and methods described and illustrated herein may beimplemented in hardware specifically configured for the monitoring andprotection of electric power delivery systems. In one embodiment, thesystems and methods herein may be implemented as intelligent electronicdevices (IEDs) in communication with the electric power delivery system.An IED according to several embodiments herein may include inputs forreceiving electric power system signals corresponding with the electricpower delivery system. For example, the IED may include an input inelectrical communication with a current transformer, potentialtransformer, or other similar device configured to obtain electric powersystem signals from a portion of the electric power delivery system andtransmit the signals to the IED.

Additional understanding of the embodiments of the disclosure can begained by reference to the drawings, wherein like parts are designatedby like numerals throughout. It will be readily understood that thecomponents of the disclosed embodiments, as generally described andillustrated in the figures herein, could be arranged and designed in awide variety of different configurations. Thus, the followingdescription of the embodiments of the systems and methods of thedisclosure is not intended to limit the scope of the disclosure, asclaimed, but is merely representative of possible embodiments of thedisclosure. In addition, the steps of a method do not necessarily needto be executed in any specific order, or even sequentially, nor need thesteps be executed only once, unless otherwise specified or contextuallyrequired.

FIG. 1A illustrates an example of an IED 100 according to several of theembodiments described herein. The IED 100 includes a voltage input forreceiving electric power system signals from a potential transformer orthe like, and a current input for receiving electric power systemsignals from a current transformer or the like. The signals may bereceived by a signal processing module 110 that may include transformers102, 114, A/D converter(s) 118, filters, and the like to produceelectric power system signals useful for the processor 124 via bus 122.The IED 100 may include a time input 112 configured to receive a commontime signal among a certain subset of IEDs and other devices. The commontime signal may be a global navigation satellite system (GNSS) timesignal, a terrestrial common time signal, a network time signal, or thelike.

The IED 100 may include a monitored equipment interface 108 forcommunication with power system equipment. The monitored equipmentinterface 108 may be configured to interface with a circuit breaker,recloser, capacitor bank, voltage regulator, reactor, or the like forcontrolling operation of the equipment. The IED 100 may include acommunications interface 116 for communication with other IEDs, or otherdevices. In one embodiment, IED 100 may be in communication with localequipment at a local location of the electric power system via thevoltage and current inputs, while being in communication via thecommunication interface 116 with another IED at a remote location of theelectric power delivery system. Thus, IED 100 may obtain electric powersystem conditions, operation information, and other communicationsrelated to a remote location of the electric power delivery system.

The IED 100 may include a computer-readable storage medium 126 forpermanent and temporary storage of information. The computer-readablestorage medium 126 may include a database 128, that may be a repositoryof settings, thresholds, and the like, useful for the operation of theIED 100. The IED 100 may further include a computer-readable storagemedium 130 that includes several operating modules that when executed onthe processor 124 cause the IED 100 to perform certain functions relatedto the monitoring and protection of the electric power delivery system.Each of the signal processing module 110, computer readable storagemedia 126, 130, time input 112, monitored equipment interface 108,communications interface 116, processor 124, and other modules may be incommunication using a data bus 142.

The computer-readable storage medium 130 may include several modulesoperable on the processor 124. One such module may be a communicationmodule 132 that includes instructions related to the transmission andreceipt of communications. The fault detector module 134 may includeinstructions related to detecting faults on the electric power deliverysystem using measurements obtained by the signal processing module 110and/or from another IED via the communications interface 116. The faulttype module 138 may be configured to determine a fault type (e.g.single-phase, multiple-phase, phase-to-phase, phase-to-ground, and thelike) from available fault information. The data acquisition module 140may include instructions related to treatment of the signals from thesignal processing module 110 to produce data useful for other modules.

The traveling wave location module 144 may include instructions and/orelectrical components to implement several of the systems, subsystems,and operations described herein. For example, traveling wave locationmodule may be configured to locate a fault using traveling waves from asingle end of the electric power delivery system. The traveling wavelocation module 144 may be embodied within the computer-readable storagemedium 130 and/or implemented as a stand-alone IED with subcomponents,modules, and inputs implemented in software, firmware, and/or hardware.

The protection action module 152 may include instructions for taking aprotective action based on a detected fault and fault location. Forexample, for a fault within a selected zone of protection, theprotection action module 152 may be configured to command a circuitbreaker to open (via the monitored equipment interface 108) to clear afault.

A fault locator system may utilize a traveling wave single-end faultlocation (TWSEFL) algorithm to estimate a fault location usingsingle-end traveling wave measurements and evaluations. The TWSEFLalgorithm may use fault location estimations from the multi-endtraveling wave fault location (TWMEFL) information and/orimpedance-based fault location (ZFL) algorithms to develop an initialguess, m_ini. If the estimations of TWMEFL algorithm or ZFL algorithmare not available, the TWSEFL algorithm can still be used to estimatethe fault location based on the traveling wave arrival times at a localterminal using an initial guess, m_ini, set to a default value (e.g.,0.5 in per unit length).

FIG. 1B illustrates a block diagram 170 of the inputs 180, parameters185, and outputs 190 of the TWSEFL algorithm 175 that may be implementedby a fault locator system (e.g., IED 100 in FIG. 1A, as part oftraveling wave location module 144 in FIG. 1A, and/or as an independentsystem). Inputs 180 may include any combination of: a vector of peaktimes (TPK or ILTPIC), a traveling wave based multi-end fault location(TWMEFL) estimate, an impedance-based multi-end fault location (ZMEFL)estimate, an impedance-based single-end fault location (ZSEFL) estimate,and a phase-to-phase fault (PPFLT) indicator.

Parameters 185 may include any combination of: traveling wave linepropagation time (TWLPT), line length (LL), single-ended traveling wavefault location observation window factor (TWOBSW), single-endedtraveling wave fault location observation window 1 (TWTOL1), andsingle-ended traveling wave fault location observation window 2(TWTOL2). In some embodiments, some parameters may be user-input basedon system conditions and some parameters may be dynamically calculatedby the system instead of provided as an input. For example, the TWOBSWmay be automatically set to 2.4, such that the observation window isequal to 2.4 times a TWLPT parameter. Similarly, the TWLPT parameter maybe input as a parameter and/or may be automatically calculated based onan input LL and known system conditions/materials. Outputs 190 of theTWSEFL algorithm may include one or more traveling wave based single-endfault location estimations (TWSEFL1, TWSEFL2, TWSEFL3, and TWSEFL4).Alternatively, a single traveling wave single-ended fault location,TWSEFL, may be output based on the hypothesis determined to be mostaccurate.

FIG. 2 illustrates a Bewley lattice diagram 200 that includes a localterminal, L, 210 and a remote terminal, R, 250 that are 1 line lengthunit apart. A fault at location 220 is at a relative distance m (perunit) from the local terminal 210 and a relative distance 1-m from theremote terminal 250. A substation B 240 is also shown. The Bewleylattice diagram 200 illustrates the traveling current waves from thefault location 220 and the various reflections from the local terminal210 and the remote terminal 250.

t₁ is the arrival time (i.e., TPK) of the first received traveling wavefrom the fault at location 220. t₂ is the arrival time of a travelingwave from the substation 240 behind the local terminal 210. t₃ is thearrival time of a traveling wave that traveled from the fault atlocation 220 to the remote terminal 250 and was reflected back to thelocal terminal 210. t₄ is the arrival time of the first traveling waveafter having been reflected by the local terminal 210, back to the faultat location 220, and then back to the local terminal 210. t₅ is relatedto reflections between the substation 240 and the fault at location 220.Finally, t₆ is the arrival time of a traveling wave that traveled fromthe fault at location 220 to the local terminal 210, from the localterminal 210 to the remote terminal 250, and from the remote terminal250 back to the local terminal 210.

The arrival times of t₃ and t₄ are considered “companion travelingwaves” because the relative time between their arrival times (TPKs) iscalculatable based, at least in part, on the distance between the localterminal 210 and the remote terminal 250. By identifying the origin orreflection path of received traveling waves and/or traveling wavepatterns, the system can estimate an accurate distance between the localterminal 210 and the location of the fault 220.

The fault at location 220 is a distance m (in per unit length) from thelocal terminal 210, so the first traveling wave is received at time t₁that is equal to m*TWLPT. Another traveling wave should return from theremote terminal 250 at the time t₃ that is equal to (2−m)*TWLPT. Thedifference between these two times is 2*(1−m)*TWLPT. Thus, one“companion traveling wave” is expected at t₁+2*(1−m)*TWLPT, which isequal to t₃. The first reflection from the fault is expected at time t₄,which is equal to t₁+2*m*TWLPT.

The timing and polarities of the traveling waves that are spaced by2*m*TWLPT and 2*(1−m)*TWLPT may be evaluated. Each reflection from adiscontinuity behind the local terminal 210 (e.g., from substation 240)may generate a traveling wave (a “test traveling wave”) toward thefault. Consequently, the system may expect multiple pairs of travelingwaves that are spaced by 2*m*TWLPT. Multiple possible traveling wavepairs may be evaluated to identify the distance to the fault, m. Thetime distance between pairs of traveling waves that occurs mostfrequently may be determined to be equal to 2*m*TWLPT.

The system may implement the TWSEFL algorithm by identifying a pluralityof valid traveling waves at the local terminal 210 that are within anobservation window that is at least two times the TWLPT (e.g.,2.4*TWLPT). The first TPK value at t₁ may be referred to as TPK(0).

FIG. 3 illustrates inputs 320 and parameters 330 received for performingoperations of a method 300 to calculate a fault location. For example, afault location system may implement the TWSEFL algorithm by identifyingarrival times (TPKs) (i.e., time stamps) of traveling wave amplitudepeaks (VPKs) of traveling waves that correspond to the mode thatincludes the maximum amplitude within an observation window defined by afunction of the TWOBSW parameter and the TWLPT (e.g., TWOBSW*TWLPT). Forexample, the TWOBSW may be 2.4 such that the observation window is equalto 2.4 times the traveling wave line propagation time, TWLPT.

A first TPK value corresponding to the first received VPK within theobservation window can be used as a reference traveling wave, and allother TPK values can be referenced, at 340, with respect to TPK(0), suchthat for each of the TPK values TPK(0) to TPK(n), a referenced TPK valuecan be calculated as follows for each value of X for X=0 to n where n isthe number of reflections:

TPK _(Ref.)(X)=TPK(X)−TPK(0)  Equation 1

A TPK vector (or set of TPK values) can be formed that includes thereferenced TPK values below a threshold, t_(limit). Input parameters 330can used to establish the threshold, t_(limit), as, for example:

t _(limit)=min(TWOBSW*TWLPT,10000 μs)  Equation 2

A set of hypotheses, H₁-H_(n), may be generated based the values in theTPK vector corresponding to VPKs that have the same polarity as the VPKcorresponding to TPK(0). In some embodiments, up to 15 hypotheses (orother arbitrary maximum number of hypotheses) may be initiallyconsidered, at 350, as hypotheses for calculating the fault location.The system evaluates each of a plurality of hypothesis TPK values todetermine if a hypothesis TPK value corresponds to the first VPKassociated with a reflection from the fault. Identify a TPK value ascorresponding to the arrival time of a VPK of the first traveling wavereflection from the fault allows for an accurate hypotheses that have atime difference relative to TPK(0) greater than a function of the TWLPTmay be discarded. For example, hypotheses that have a time differencerelative to TPK(0) greater than 2·TWLPT+10 microseconds may bediscarded. If no hypotheses exist, at 360, then no estimated TWSEFL maybe generated, at 365.

If there are a plurality of hypotheses and inputs for TWMEFL, ZMEFL orZSEFL are available, at 370, then one or more of the inputs for TWMEFL,ZMEFL or ZSEFL may be used to as an initial estimate of a faultlocation, m_ini. In various embodiments, the following priority may beutilized for determining, at 380, an initial estimate of the faultlocation, m_ini: TWMEFL, ZMEFL, and then ZSEFL. In other embodiments, adifferent priority may be utilized and/or a weighted average ofestimates based on one or more of TWMEFL, ZMEFL, and ZSEFL. If none ofTWMEFL, ZMEFL or ZSEFL is available, at 370, then a default initialestimate may be used, at 385 (e.g., the middle of the line).

FIG. 4 illustrates an example of a method 400 of one embodiment ofcalculating a fault location TWSEFL1. As described above, if TWMEFL isavailable, at 410, then the hypothesis for the fault location (based ona hypothesis TPK as described herein) that is closest to the TWMEFLestimation is used, if it is within the TWTOL2 parameter, at 415. If aTWMEFL estimation is not available, at 410, but a ZMEFL estimate isavailable, at 420, then the system may utilize the hypothesis TPK thatresults in a fault location calculation that is within a predeterminedrange (e.g., 3%) of the ZMEFL estimate, at 425. If both the TWMEFL andZMEFL estimations are unavailable, but a ZSEFL estimation is availableand a phase-to-phase fault is indicated, at 430, then the hypothesisthat results in a fault location calculation within a predeterminedrange (e.g., 5%) of the ZSEFL estimate may be utilized.

As long as the hypothesis are within allowable limits, at 450, based oninput parameters, then the selected hypothesis is used to calculate thefault location TWSEFL1, at 460. If none of the three estimations(TWMEFL, ZMEFL, and ZSEFL) are available, at 445, and/or none of thehypotheses are within allowable limits, at 455, then a fault locationmay be estimated based on a selected hypothesis TPK as described below.

In other embodiments, estimates and/or inputs from TWMEFL, ZMEFL, and/orZSEFL may not be provided and/or considered in determining a faultlocation. In such instances, a fault location may be calculated based ona selected hypothesis as described below.

FIG. 5 illustrates a portion of a method 500 for calculating a faultlocation using a ruler evaluation approach, also referred to as arepeating travel time RTT evaluation approach. For each hypothesis TPK,a fault reflection value corresponding to 2*m may be calculated, at 502,as the difference between the hypothesis TPK value and TPK(0), whereTPK(0) is the arrival time of the first received traveling wave peak(VPK). For a given hypothesis, H, the equation may be represented as:

F(H)=TPK(H)−TPK(0).  Equation 3

For each hypothesis, H, a remote reflection value corresponding to thearrival time (TPK) of a traveling wave peak (VPK) from a remote location(e.g., the second end of the power line) may be calculated, at 504, fora given hypothesis, H, that corresponds to 2*(1−m) as:

R(H)=2*TWLPT−F(H).  Equation 4

FIG. 6A illustrates a Bewley lattice diagram showing TPK(0) 611, F(1)612, and R(1) 613, where F(1) 612 and R(1) 613 are based on the firsthypothesis TPK(1). The time difference between TPK(1) and TPK(0), F(1)is equal to 2*m*TWLPT, per Equation 3 above. R(1) is a calculated usingEquation 4 as an expected reflection assuming the hypotheses TPK(1) is acorrect hypothesis. The expected R(1) 613 reflection can be thought ofas a “companion traveling wave” that, assuming the hypothesis TPK(1) isaccurate, should correspond to one of the received TPK values. If nosuch TPK value is detected (i.e., no match is found), then a confidencelevel that the hypothesis is correct is decreased, as described below.

Returning to FIG. 5, the system may create a time difference vector, DT,that include all of the possible time differences using all TPKs in theobservation window. That is, a set of time differences (DT set) or atime difference vector (DT) may be generated to include a plurality ofdifference elements. The difference elements included in the DT set (orDT vector) include all difference between all pair-combinations of TPKs.As a specific example: if the TPKs received during the observationwindow are A, B, C, D, E, and F, where A corresponds to the arrival timeof the first traveling wave peak (VPK), then the DT set will includedifferences: (A-B), (A-C), (A-D), (A-E), (A-F), (B-C), (B-D), (B-E),(B-F), (C-D), (C-E), (C-F), (D-E), (D-F), and (E-F). The differences inthe set may be expressed as absolute values and/or evaluated for matchesindependent of sign.

The system may determine, at 508, a count of the number of instances,NM(H), that the time differences in the vector DT match the calculatedF(H). A match may be defined as a number that is within a predefinedtolerance range, as defined by, for example, the TWTOL1 parameter (e.g.,TWTOL1=10 μs). A first error, ERRM(H), may be calculated, at 510, foreach hypothesis that corresponds to the NM(H) set.

The fault location system may determine, at 512, the number ofinstances, N1_M(H), that the time differences in the vector DT match thecalculated R(H). Again, a match may be considered valid only if it is anexact match or if numbers are within a predefined tolerance range. Asecond error, ERR1_M(H), may be calculated, at 514, for each hypothesisthat corresponds to the N1_M(H) set. A total error, ERR(H), may becalculated, at 516, by adding ERRM(H) and ERR1_M(H).

FIG. 6B illustrates traveling waves in dashed lines that are caused byreflections for a substation 640 that the system may utilize todetermine the number of instances NM(H) and N1_M(H). One benefit of theRRT method described above is that the approach leverages availablereflections from the external elements behind the local terminal (e.g.,substation 240, FIG. 2).

Without exhaustively repeating the discussion above for the TPKsassociated with the dashed lines in FIG. 6B, it is visually clear thatthe TPKs at the local terminal 610 corresponding to the dashed lines aresimilar to the solid lines discussed above for TPK(0) 611, F(1) 612, andR(1) 613, except the dashed lines are shifted downward in time by anamount of time equal to two times the traveling wave propagation betweenthe local terminal L 610 and the point B in the substation 640.

FIG. 7 illustrates a method for calculating expected traveling waves(ETW) for each hypothesis. FIG. 7 also includes operations forevaluating each hypothesis using weighted values from the RRT and ETWapproaches. The system may implement the ETW approach by calculating, at718, a vector of expected traveling wave arrival times, Th, for eachhypothesis. A set of ETWs may be used as an equivalent or similar datastructure for a number of ETW elements. The vector of expected travelingwave arrival times, Th, may be based on: the distance to the fault, m;the TWLPT parameter; and the threshold, t_(limit), from Equation 2. Avector of expected traveling wave arrival times, Th, may be calculatedfor each hypothesis based on a number of traveling wave sets as, forexample:

{right arrow over (T_(h))}=[TLSET1,TLSET2,TLSET3,TLSET4]−TLSET1(1)  Equation 5

The vector of expected traveling wave arrival times, Th, may includeonly those expected traveling waves within each of TLSET1, TLSET2,TLSET3, and TLSET4 that are within an observation window. TLSET1corresponds to a pattern of TPK values for reflections from the fault tothe local terminal, back to the fault, and then back to the localterminal (i.e., fault-local-fault-local).

FIG. 8A illustrates a fault-local-fault-local traveling wave reflectionpattern with the fault at location m=0.3 pu on a 100-mile line (i.e.m=30 miles) with the TWLPT equal to 540 μs. Thus, the system maycalculate TLSET1 as follows:

TLSET1=k*m*TWLPT,k=1,3,5, . . .  Equation 6

TLSET2 corresponds to the pattern of TPK values for reflections from thefault to the remote terminal, back to the fault, and then to the localterminal (i.e., fault-remote-fault-local).

FIG. 8B illustrates a fault-remote-fault-local traveling wave reflectionpattern with similar parameters to the line in FIG. 8A. Thus, the systemmay calculate TLSET2 as follows:

TLSET2=2*k*(1−m)*TWLPT,k=1,2,3, . . .  Equation 7

TLSET3 corresponds to the pattern of TPK values for reflections from thelocal terminal to the fault, to the remote terminal, back to the fault,and to the local terminal (i.e., local-fault-remote-fault-local).

FIG. 8C illustrates a local-fault-remote-fault-local traveling wavereflection pattern with similar parameters to the line in FIG. 8A. Thesolid line represents the first TLSET3 pattern. The dashed linesrepresent subsequent TLSET3 patterns. The system may calculate TLSET3 asfollows:

TLSET3=[k*m+2]*TWLPT,K=1,3,5, . . .  Equation 8

TLSET4 corresponds to the pattern of TPK values for reflections from thefault to the local terminal, to the fault, to the remote terminal, backto the fault, back to the remote terminal, back to the fault, and thento the local terminal (i.e.,fault-local-fault-remote-fault-remote-fault-local). Without belaboringthe point with yet another drawing, the system may calculate TLSET4 asfollows:

TLSET4=[k*M+2(2−M)]*TWLPT,K=1,3,5, . . .  Equation 9

Once the elements of TLSET1, TLSET2, TLSET3, and TLSET4 have beenidentified, the vector of expected traveling wave arrival times, Th, (ora set of ETWs) may be generated by filtering out elements with the samevalue, and elements that have values outside of the observation window.The elements in the vector of expected traveling wave arrival times, Th,may be sorted in ascending order to facilitate comparisons and/ordecrease computations processing times.

FIG. 9 illustrates all the expected TPK values in the vector of expectedtraveling wave arrival times, Th, for a hypothesis TPK associated with afault location estimated at m=0.3.

Turning again to FIG. 7, the fault location system may then determine,at 720, a count of the number of TPKs in the TPK vector that match thevector of expected traveling wave arrival times, Th. Again, a match maybe defined as an exact match or as a match within a tolerance range,such as a tolerance ranged defined by the TWTOL2 parameter. The numberof matches or scores may be referred to as NS(H). in some embodiments,an event error, ERR_S(H) may be calculated as well.

The results of the RTT and/or EWT approaches may be evaluated to selecta hypothesis as correct. The system may select a correct hypothesisbased on a weighted function of the results of the RTT and/or EWTapproaches and may optionally consider the respective errorcalculations. In embodiments that use both the ruler and the scoreevaluation approaches, the system may assign, at 722, a weighting factorWGHT(H) equal to NS(H) if the R(H) of each respective hypothesiscorresponds to a TPK value within the TPK vector. Otherwise, the WGHTfactor for a given hypothesis may be assigned to zero/null

For each hypothesis, a sum N(H) may be calculated, at 724, as follows:

N(H)=NM(H)+N1_M(H)+WGHT(H).  Equation 10

An error per event may be calculated, at 726, as follows:

$\begin{matrix}{{{ERRpu}(H)} = \frac{\left( {{{ERR}(H)} + {ERR\_ S}} \right)}{N(H)}} & {{Equation}\mspace{14mu} 11}\end{matrix}$

In other embodiments that use only the score or ETW evaluation approach,Equation 10 may be modified to ignore NM(H) and N1_M(H) and theweighting factor WGHT(H) may be unrelated to the match of R(H) valueswith TPK values within the TPK vector. Thus, for each hypothesis beingevaluated by only the score evaluation approach, an equation for N(H)may be expressed as:

N(H)=NS(H)  Equation 10.1

A fault location error of the initial estimate, FLERR, may bedetermined, at 728. For example, the FLERR may be determined as thegreater of either 0.2 pu or three times the reciprocal of the linelength. The power line may be conceptually divided, at 730, into threesections. The initial guess, m_ini, can be defined as being in one ofthe three sections as follows, for example:

-   -   Section 1: m_ini<(1/2−FLERR);    -   Section 2: (1/2−FLERR)<=m_ini<=(1/2+FLERR); and    -   Section 3: m_ini>(1/2+FLERR).

FIG. 10 continues the method of FIG. 7 and branches, at 1032, based thesection within which m_ini is located. For instance, if m_ini is inSection 1, at 1034, then the hypothesis with the greatest NM is used. Ifthere are equal values of NM, N1_M can be used to order the hypothesesin descending order. If there are an equal number of N1_M values, thenthe ERRpu can be used to order the hypotheses in ascending order.

If m_ini is in Section 3, at 1036, the hypothesis with the greatest N1_Mis used. If there are equal values of N1_M, NM can be used to order thehypotheses in descending order. If there are an equal number of NMvalues, then the ERRpu can be used to order the hypothesis in ascendingorder.

If m_ini is in Section 2, at 1038, the hypothesis with the greatest N isused. If there are equal values of N, then the ERRpu can be used toorder the hypothesis in ascending order.

The fault location system can then calculate, at 1040, TWSEFLn, based onthe ordered hypotheses, where n=1, 2, 3 and 4 as:

$\begin{matrix}{{TWSEFLn} = \frac{{LL}*{DTn}}{2*{TWLPT}}} & {{Equation}\mspace{14mu} 12}\end{matrix}$

Using the F(H) notation described above, Equation 12 can alternativelybe expressed as:

$\begin{matrix}{{TWSEFLn} = \frac{{LL}*{F(H)}}{2*{TWLPT}}} & {{Equation}\mspace{14mu} 12.1}\end{matrix}$

If m_ini is in Section 1, the calculated distance to the fault, m,should be less than 0.3, or it is set to N/A. If m_ini is in section 3,the calculated distance to the fault should be between 0.7 and 1.0, orit is set to N/A.

FIG. 11 provides a schematic diagram 1100 for a simulation to illustratea specific example of the systems and methods described herein. Thedescription below uses actual data from a simulation of the schematicdiagram 1100 and is intended to provide a specific example of thesystems and methods described above and is not intended to be limitingin any way.

The schematic diagram 1100 simulates an AG fault at 30% of a 100-miletransmission line with a TWLPT of 540 μs. The schematic diagram 1100also includes two 25-mile parallel lines connected to the two-lineterminals (TWLPT=135 μs) and two sources behind the parallel lines.

FIG. 12 illustrates the alpha currents 1200 after being processed by adifferentiator smoother for the simulated fault with the correspondingVAL or FAL indication for each peak. VAL or FAL value of logic oneindicates that the traveling wave peak is a suitable input for theTWSEFL algorithm.

The data acquisition circuitry (including, for example, data acquisitionmodule 140, FIG. 1A) obtains the time stamps from alpha signal A 1201,alpha signal B 1202, and alpha signal C 1203. For this line, theobservation window of the data buffer may be, for example, 2.4*TWLPT(2.4*540 μs=1296 μs). For the signals in FIG. 12, the data bufferprovides the following outputs:

For alpha signal A 1201:

-   -   IATP=[51074, 51344, 51398, 51613, 51668, 51830, 51883, 51938,        51992, 52100, 52207, 52262].        -   IAVAL=[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]        -   IAFAL=[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

For alpha signal B 1202:

-   -   IBTP=[51074, 51344, 51398, 51613, 51668, 51830, 51830, 51938,        51992, 52100, 52207, 52262].    -   IBVAL=[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]    -   IBFAL=[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

For alpha signal C 1203:

-   -   ICTP=[51074, 51344, 51398, 51613, 51668, 51830, 51830, 51938,        51992, 52100, 52207, 52262].    -   ICVAL=[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]    -   ICFAL=[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

The system may calculate the raw time stamps, ITP, in microseconds asfollows:

$\begin{matrix}{{ITPn} = \frac{\begin{matrix}{{{IATPn} \cdot \left( {{IAVALn} + {IAFALn}} \right)} + {{IBTPn} \cdot}} \\\left( {{IBVALn} + {IBFALn} + {{ICTPn} \cdot \left( {{ICVALn} + {ICFALn}} \right)}} \right.\end{matrix}}{\begin{matrix}{\left( {{IAVALn} + {IAFALn}} \right) + \left( {{IBVALn} + {IBFALn}} \right) +} \\\left( {{ICVALn} + {ICFALn}} \right)\end{matrix}}} & {{Equation}\mspace{14mu} 13}\end{matrix}$

In Equation 13 above, n is the index referring to the correspondingrecord. In the illustrated embodiment, the system determines 12 recordswith the following time stamps: ITP=[51074, 51344, 51398, 51613, 51668,51830, 51883, 51938, 51992, 52100, 52207, 52262].

The system identifies that the first traveling wave peak (VPK) isreceived at an arrival time (TPK) equal to 51074 μs in mode 1,corresponding to the alpha mode. As described above, close-proximitypeaks are removed by removing values within close proximity (e.g., asdefined by a TWDSW parameter, such as 10 μs) of the identified firsttraveling wave. Because the next ITP value (51344) is more than 10 μsfrom the identified first traveling wave, no ITP values are filtered.

The resulting ENUM (modal number) is 1, which indicates the fault is anAG fault. The system retrieves all three phase currents and reconstructsthe alpha traveling wave signals. Using these signals, the algorithminterpolates the raw time stamps ITP, which are in microseconds, toobtain more precision with interpolated ITPI time stamps in nanoseconds.In some embodiments, if the interpolated ITPI data is different than theraw ITP data by more than a threshold amount (e.g., 2 μs), then the ITPdata may be used instead.

FIG. 14 illustrates a table with the interpolated time stamps ITPI, andtheir corresponding estimated magnitudes, IMAG, for the simulation. Thesystem may reference the interpolated TPKs (ITPIs) to the firsttraveling wave time stamp as illustrated in FIG. 15.

The system may then determine the sign TPSIGN of each peak with respectto the first VPK using the signed VPK value of each peak, as illustratedin FIG. 16.

The system may then generate a time difference vector, DT, from theinterpolated TPK vector. The time difference vector, DT, may beequivalently described as a set of time difference values, DT, insteadof as a vector. The length of the time difference vector, DT,corresponds to the number of combinations of TPKs taken two at a time(i.e., pair-combinations). Thus, the length of the time differencevector is: (11+1)*11/2=66). For this simulation, the time differencevector, DT, is:

-   -   DT=[53.348, 53.961, 54.066, 54.082, 54.156, 54.191, 107.453,        107.539, 108.152, 108.453, 161.500, 161.609, 162.414, 162.438,        215.785, 215.797, 215.906, 216.520, 216.605, 269.863, 269.867,        269.867, 269.879, 269.953, 269.977, 270.031, 270.063, 323.938,        323.945, 324.023, 324.059, 324.059, 324.098, 377.406, 378.020,        378.215, 431.563, 432.316, 432.391, 485.664, 486.383, 486.473,        539.730, 539.844, 539.855, 539.895, 593.816, 593.922, 593.926,        593.977, 594.000, 647.883, 648.082, 702.270, 756.336, 756.414,        809.723, 809.762, 863.789, 863.879, 863.953, 917.914, 917.945,        1026.367, 1133.820, 1187.977].

Based on the polarity check and the TWLPT, the first reflection fromfault should be less than 2*TWLPT+10 μs (i.e., 2*540+10=1090 μs), wherethe 10 μs represents an example threshold for increasing inclusivity. Inthis case, the system identifies three hypotheses (underlined and boldedin FIG. 16).

The system may utilize the ruler evaluation approach and/or the scoreevaluation approach to detect valid reflections. Using the rulerevaluation (RTT evaluation) approach for each hypothesis, the systemcalculates two time references. A first reference corresponds to thereflection from the fault, F(H), and the second reference corresponds tothe reflection from the remote terminal, R(H).

As illustrated in FIG. 17, the reflection from the fault F(H) for thefirst hypothesis is F(1)=324.098 and the associated reflection from theremote terminal R(H) for the first hypothesis is R(1)=755.902. Thesystem may count the number of matches of F(H) with time differences inthe time difference vector DT to determine NM(H), and count the numberof matches of R(H) with time differences in the time difference vectorDT to determine N1_M(H). As illustrated, in FIG. 17, there are sixmatches for F(H) in the time difference vector DT and two matches forR(H) in the time different vector DT for the first hypothesis. The sixmatches for F(H) are underlined in the DT vector above. The two matchesfor R(H) are double underlined in the DT vector above. The system mayalso calculate the total errors for NM(H) and N1_M(H) within TWTOL1, asshown in FIG. 18.

In some embodiments, a hypothesis may be selected as “correct” or as the“best” hypothesis based on the hypothesis having the greatest number ofNM matches, the greatest number of N1_M matches, and/or the greatesttotal number of matches NM+N1_M. In other embodiments, the scoreevaluation (ETW evaluation) approach may be used in addition to theruler or RTT evaluation approach to select a “correct” or “best”hypothesis. In still other embodiments, the score evaluation (ETWevaluation) approach may be used by itself without the ruler or RTTevaluation approach. In such an embodiment, the weighting of the scoresNS(H) based on a TPK match for R(H) would be irrelevant and so would beignored and/or not calculated (See, e.g., Equation 10.1).

Regardless, a selected hypothesis may be used to calculate a location ofthe fault relative to the local terminal. Whether the RRT method is usedalone or in combination with the ETW evaluation approach, a hypothesiscan be selected based on a function of the NM and NM_1 values for eachof the evaluated hypotheses.

Using the score evaluation (ETW evaluation) approach, a set or vector ofexpected traveling wave arrival times, Th, is determined that includes aplurality of expected arrival times of traveling waves (ETWs) for eachhypothesis. The ETWs are compared with the actual received TPK values inthe TPK vector to identify matches that are within TWTOL2 (e.g. TWTOL2=5μs). In some embodiments, when the system creates the vector of expectedtraveling wave arrival times, Th, the system may remove close-proximityvalues.

FIG. 19 shows the TPK matches for each hypothesis per the associatedvectors of expected traveling wave arrival times, Th. The expectedtraveling wave arrival times are in the third, fourth, and fifth columnscorresponding to the vectors of expected traveling wave arrival times,Th, for each of the first, second and third hypotheses, respectively.The expected times corresponding to F(H) are underlined, and theexpected times corresponding to R(H) are double underlined. Thestrikethrough values are the values that are within TWDSW and may beremoved or not considered. The boxed and bolded value can be used forsupervision of R(H).

FIG. 20 shows the measured TPKs and the expected traveling waves foreach of the three hypotheses. Matches are identified between the TPKmeasurements and the calculated hypotheses of the vector of expectedtraveling wave arrival times, Th. The circles identify the matchesbetween TPK and hypotheses within TWTOL2 (5 μs in this simulation).

FIG. 21 illustrates a table showing the number of matches/scores NS(H)for each hypothesis.

FIG. 22 illustrates the total errors for NS(H) within TWTOL2 (e.g. 5μs), as calculated by the system.

The system may identify one or more matches between R(H) and F(H) withinTWTOL1 (e.g. 10 μs) for a corresponding hypothesis. For example, ifF(H)=324.098, R(H)=2*TWLPT−F=2*540−324.098=755.902. The system mayidentify 756.414 in the TPK column (boxed and bolded in FIG. 14) andthen NS(H)=2(matches)*1 (supervision logic)=2.

FIG. 23 is a table showing the weight (WGHT) for each hypothesis basedon a match of R(H) with a received TPK. In embodiments in which thescore algorithm is used in combination with the ruler algorithm, theoutput of the score algorithm may be weighted based on a match of R(H)with a received TPK. In embodiments in which the score evaluationapproach is used alone, no such weighting may be available or used.

The variable N can be defined as a figure of merit that indicates howclosely the received TPKs match the expected TPKs for a fault locationcalculated based on a given hypothesis. The N values can be calculatedusing Equation 10 above. A total per unit error can also be calculatedfor each hypothesis using Equation 11 above.

FIG. 24 includes a table with the N values and the total per unit error,ERRpu, for each of the three hypotheses.

As previously described, the system may define three line sections asfollows:

-   -   Section 1: m_ini<0.3    -   Section 2: 0.3<=m_ini<=0.7; and    -   Section 3: m_ini>0.7,

As described above, the default initial guess when other data isunavailable is m_ini=0.5, and so the m_ini falls within Section 2.Therefore, the system assumes that the fault is in Section 2. For faultsin Section 2, the algorithm uses N (and optionally ERRpu in the event ofa tie) to order the hypotheses, as follows: TWSE=[0.3, 0.8, 0.95, NA].

The traveling wave single-ended fault location, TWSEFL, for hypothesis 1can be calculated per Equation 12.1 above as:

TWSEFL ₁ =LL*F(1)/2*TWLPT=(100*324.098)/(2*540)=30.009 miles.

FIG. 25 shows the expected reflections for a fault at m=0.3 and the TPKmeasurements shown with circles that match the received TPK values abovefor this simulation.

In some cases, well-known features, structures or operations are notshown or described in detail. Furthermore, the described features,structures, or operations may be combined in any suitable manner in oneor more embodiments. It will also be readily understood that thecomponents of the embodiments as generally described and illustrated inthe figures herein could be arranged and designed in a wide variety ofdifferent configurations.

Several aspects of the embodiments described may be implemented assoftware modules or components. As used herein, a software module orcomponent may include any type of computer instruction or computerexecutable code located within a memory device and/or transmitted aselectronic signals over a system bus or wired or wireless network. Asoftware module or component may, for instance, comprise one or morephysical or logical blocks of computer instructions, which may beorganized as a routine, program, object, component, data structure,etc., that performs one or more tasks or implements particular abstractdata types.

In certain embodiments, a particular software module or component maycomprise disparate instructions stored in different locations of amemory device, which together implement the described functionality ofthe module. Indeed, a module or component may comprise a singleinstruction or many instructions, and may be distributed over severaldifferent code segments, among different programs, and across severalmemory devices. Some embodiments may be practiced in a distributedcomputing environment where tasks are performed by a remote processingdevice linked through a communications network. In a distributedcomputing environment, software modules or components may be located inlocal and/or remote memory storage devices. In addition, data being tiedor rendered together in a database record may be resident in the samememory device, or across several memory devices, and may be linkedtogether in fields of a record in a database across a network.

Embodiments may be provided as a computer program product including anon-transitory computer and/or machine-readable medium having storedthereon instructions that may be used to program a computer (or otherelectronic device) to perform processes described herein. For example, anon-transitory computer-readable medium may store instructions that,when executed by a processor of a computer system, cause the processorto perform certain methods disclosed herein. The non-transitorycomputer-readable medium may include, but is not limited to, harddrives, floppy diskettes, optical disks, CD-ROMs, DVD-ROMs, ROMs, RAMs,EPROMs, EEPROMs, magnetic or optical cards, solid-state memory devices,or other types of machine-readable media suitable for storing electronicand/or processor executable instructions.

While specific embodiments and applications of the disclosure have beenillustrated and described, it is to be understood that the disclosure isnot limited to the precise configurations and components disclosedherein. For example, the systems and methods described herein may beapplied to an industrial electric power delivery system or an electricpower delivery system implemented in a boat or oil platform that may notinclude long-distance transmission of high-voltage power. Moreover,principles described herein may also be utilized for protecting anelectric system from over-frequency conditions, wherein power generationwould be shed rather than load to reduce effects on the system.Accordingly, many changes may be made to the details of theabove-described embodiments without departing from the underlyingprinciples of this disclosure. The scope of the present invention(s)should, therefore, be interpreted to encompass at least the followingclaims:

1. A system to determine a relative location of a fault in a power lineof an electric power delivery system comprising: a traveling wavedetector to: detect an arrival time (TPK) and associated peak amplitude(VPK) of each of a plurality of traveling waves received at a firstlocation on the power line, and identify hypothesis TPKs as TPKscorresponding to traveling waves detected after a first detectedtraveling wave that have the same polarity as the first detectedtraveling wave; and a fault location determination subsystem comprisingat least one processor and a memory to: calculate a set of expectedtraveling wave arrival times (ETWs) for each hypothesis; determine afirst number of matches (NS) of the ETWs of each hypothesis with thedetected TPKs; calculate a merit value (N) of each of the hypothesesbased on a function of the number of matches (NS) of each respectivehypothesis; select one of the hypotheses based on the merit value (N);and calculate a location of the fault relative to the first locationbased on the length of the power line, a traveling wave line propagationtime (TWLPT), and the selected hypothesis.
 2. The system of claim 1,wherein the traveling wave detector is configured to detect the TPKs andcorresponding peak amplitude VPKs of each of the traveling wavesdetected within an observation window.
 3. The system of claim 1, whereinthe hypothesis with the greatest number of matches (NS) is the selectedhypothesis.
 4. The system of claim 1, wherein the first number ofmatches (NS) comprises identifying detected TPKs and calculated ETWsthat are within a threshold range of one another.
 5. The system of claim1, wherein the fault location determination subsystem is configured tocalculate the location of the fault based on a distance from the firstlocation to the fault location that is equal to one-half the length ofthe power line, multiplied by the selected hypothesis, divided by theTWLPT.
 6. The system of claim 1, wherein the traveling wave detector isconfigured to detect only those TPKs and VPKs of the traveling waves atthe first location on the power line within an observation window. 7.The system of claim 6, wherein the observation window includes TPKs andVPKs of traveling waves received until a time equal to TWOBSW*TWLPTafter the first received traveling wave, where TWOBSW is an observationwindow coefficient.
 8. A method of calculating a relative location of afault in a power line of an electric power delivery system comprising:detecting, via a detector, an arrival time (TPK) and peak amplitude(VPK) of each of a plurality of traveling waves at a first location onthe power line; identifying TPKs corresponding to VPKs detected after afirst detected traveling wave that have the same polarity as the firstdetected traveling wave as hypotheses; calculating, via a processor, aset of expected traveling wave arrival times (ETWs) for each hypothesis;determining a first number of matches (NS) of the ETWs of eachhypothesis with the detected TPKs; calculating a merit value (N) of eachof the hypotheses based on a function of the number of matches (NS) ofeach respective hypothesis; selecting one of the hypotheses based on themerit value (N); and calculating a location of the fault relative to thefirst location based on the length of the power line, a traveling waveline propagation time (TWLPT), and the selected hypothesis.
 9. Themethod of claim 8, wherein the hypothesis with the greatest number ofmatches (NS) has the highest merit value (N), and wherein the hypothesiswith the highest merit value (N) is the selected hypothesis.
 10. Themethod of claim 8, wherein determining the first number of matches (NS)comprises identifying detected TPKs and calculated ETWs that are withina threshold range of one another.
 11. The method of claim 8, whereincalculating the location of the fault relative to the first locationcomprises calculating a distance from the first location to the locationof the fault by multiplying one-half the length of the power line by theselected hypothesis divided by the TWLPT.
 12. The method of claim 8,wherein detecting, the TPKs and VPKs of each of the plurality oftraveling waves at the first location on the power line comprises onlydetecting those VPKs and TPKs within an observation window.
 13. Themethod of claim 12, wherein the observation window includes TPKs andVPKs received until a time equal to TWOBSW*TWLPT after the firstdetected traveling wave, where TWOBSW is an observation windowcoefficient.
 14. The method of claim 8, further comprising: calculatinga fault reflection value, F(H), for each hypothesis.
 15. The method ofclaim 14, wherein calculating the F(H) of each hypothesis comprisesdetermining a time difference between the hypothesis and the TPK of thefirst detected traveling wave.
 16. The method of claim 14, whereindetecting the TPKs of each of the traveling waves received after thefirst detected traveling wave comprises detecting each TPK relative tothe TPK of the first detected traveling wave, such that the F(H) of ahypothesis TPK is equal to the hypothesis TPK.
 17. The method of claim14, further comprising: assigning a weight factor (WGHT) to eachhypothesis equal to: the NS associated with each hypothesis for whichthe associated R(H) corresponds to one detected TPK associated with thefault reflection value F(H), and zero (0) for each hypothesis for whichthe associated R(H) value does not correspond to any detected TPKassociated with the fault reflection value F(H).
 18. The method of claim14, further comprising: calculating a remote reflection value, R(H), foreach hypothesis; determining a second number of matches (NM) of the F(H)of each hypothesis with a set of time differences (DT set) betweenpair-combinations of the detected TPKs received after the first detectedtraveling wave; and determining a third number of matches (N1_M) of theR(H) with the time differences in the DT set.
 19. The method of claim18, wherein calculating the R(H) of each hypothesis comprisesdetermining the difference between twice the TWLPT and the F(H) value ofthe respective hypothesis, such that for each hypothesis:R(H)=2*TWLPT−F(H).
 20. The method of claim 14, further comprising:assigning a weight factor (WGHT) to each hypothesis equal to: the NSassociated with each hypothesis for which the associated R(H)corresponds to one detected TPK, and zero (0) for each hypothesis forwhich the associated R(H) value does not correspond to any detected TPK;and calculating a remote reflection value, R(H), for each hypothesis;determining a second number of matches (NM) of the F(H) of eachhypothesis with a set of time differences (DT set) betweenpair-combinations of the detected TPKs received after the first detectedtraveling wave; and determining a third number of matches (N1_M) of theR(H) with the time differences in the DT set; calculating the sum of thesecond number of matches (NM), the third number of matches (N1_M), andthe weight factor (WGHT) as an adjusted merit value (N) equal to(NM+N1_M+WGHT), and wherein selecting the hypotheses based on the meritvalue (N) comprises selecting the hypothesis determined to have thehighest adjusted merit value.
 21. A computer-implemented method,comprising: detecting, via a detector, an arrival time (TPK) and peakamplitude (VPK) of each of a plurality of traveling waves at a firstlocation on the power line; and identifying TPKs corresponding totraveling waves detected after a first detected traveling wave that havethe same polarity as the first detected traveling wave as hypotheses;calculating, via a processor, a set of expected traveling wave arrivaltimes (ETWs) for each hypothesis; identifying a first number of matches(NS) of the calculated ETWs with the detected TPKs; calculating a faultreflection value, F(H), for each hypothesis; calculating a remotereflection value, R(H), for each hypothesis; determining a second numberof matches (NM) of the F(H) of each hypothesis with a set of timedifferences (DT set) between pair-combinations of the detected TPKsreceived after the first detected traveling wave; determining a thirdnumber of matches (N1_M) of the R(H) with the time differences in the DTset; selecting one of the hypothesis based on at least one of NS, NM,and N1_M; and calculating a distance from the first location to thefault location based on a function of the length of the power line, thetraveling wave line propagation time (TWLPT), and the selectedhypothesis.
 22. The computer-implemented method of claim 21, furthercomprising: determining an initial guess of a relative location of afault (m_ini) as being within one of a first, second, and third sectionof a power line; and prioritizing the hypothesis in a priority orderbased on: NM, where m_ini is determined to be within the first section,N, where m_ini is determined to be within the second section, and N1_M,where m_ini is determined to be within the third section, whereinselecting one of the hypotheses based on at least one of NS, NM and N1_Mcomprises selecting the hypothesis with the highest priority.
 23. Thecomputer-implemented method of claim 22, wherein the m_ini is determinedto be within one of the first, second, and third sections based oninformation received from one of: a multi-end traveling wave faultlocation estimation system, a multi-end impedance fault locationestimation system, and a single-end impedance fault location estimationsystem.